某一类控制系统中发生的指数偏差现象

The large deviation phenomenon on Lyapunov exponents in some class of control systems

我们考虑在某类控制系统中,以Lyapunov指数作为观测量,远离给定遍历测度的那些周期测度.对于这类周期测度的数量关于周期的指数增长率,我们将用测度熵在某个集合上的上界给出它的一个上限控制.

In some class of control systems, we consider the periodic measures whose i-th Lyapunov exponent is far from a given ergodic measure for some i. We estimate the exponential growth rate of such periodic measures and give a upper bound of the exponential growth rate by the supremum of entropy.